theorem
proved
term proof
eq_of_reflTransGen
show as:
view Lean formalization →
formal statement (Lean)
35theorem eq_of_reflTransGen {R : V → V → Prop} {f : V → ℝ}
36 (hadj : ∀ a b, R a b → f a = f b) {u v : V}
37 (huv : Relation.ReflTransGen R u v) : f u = f v := by
proof body
Term-mode proof.
38 induction huv with
39 | refl => rfl
40 | tail _ hbc ih => exact ih.trans (hadj _ _ hbc)
41
42/-- On a preconnected graph (every pair related by ReflTransGen),
43 agreement on edges implies global constancy. -/